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Derivative of f(x)=5
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Identical expressions
three *log(2x- five , four)^ seven
3 multiply by logarithm of (2x minus 5,4) to the power of 7
three multiply by logarithm of (2x minus five , four) to the power of seven
3*log(2x-5,4)7
3*log2x-5,47
3*log(2x-5,4)⁷
3log(2x-5,4)^7
3log(2x-5,4)7
3log2x-5,47
3log2x-5,4^7
Similar expressions
3*log(2x+5,4)^7

The derivative of the function/ 3*log(2x-5,4)^7

Derivative of 3*log(2x-5,4)^7

The solution

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     7            
3*log (2*x - 27/5)

$$3 \log{\left(2 x - \frac{27}{5} \right)}^{7}$$

3*log(2*x - 27/5)^7

Detail solution

The derivative of a constant times a function is the constant times the derivative of the function.
1. Let $u = \log{\left(2 x - \frac{27}{5} \right)}$ .
2. Apply the power rule: $u^{7}$ goes to $7 u^{6}$
3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \log{\left(2 x - \frac{27}{5} \right)}$ :
  1. Let $u = 2 x - \frac{27}{5}$ .
  2. The derivative of $\log{\left(u \right)}$ is $\frac{1}{u}$ .
  3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(2 x - \frac{27}{5}\right)$ :
    1. Differentiate $2 x - \frac{27}{5}$ term by term:
      1. The derivative of a constant times a function is the constant times the derivative of the function.
        
        Apply the power rule: $x$ goes to $1$
        
        So, the result is: $2$
      2. The derivative of the constant $- \frac{27}{5}$ is zero.
      The result is: $2$
    The result of the chain rule is:
    
    $\frac{2}{2 x - \frac{27}{5}}$
  The result of the chain rule is:
  
  $\frac{14 \log{\left(2 x - \frac{27}{5} \right)}^{6}}{2 x - \frac{27}{5}}$
So, the result is: $\frac{42 \log{\left(2 x - \frac{27}{5} \right)}^{6}}{2 x - \frac{27}{5}}$
Now simplify:

$\frac{210 \log{\left(2 x - \frac{27}{5} \right)}^{6}}{10 x - 27}$

The answer is:

$\frac{210 \log{\left(2 x - \frac{27}{5} \right)}^{6}}{10 x - 27}$

The graph

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The first derivative [src]

      6            
42*log (2*x - 27/5)
-------------------
     2*x - 27/5

$$\frac{42 \log{\left(2 x - \frac{27}{5} \right)}^{6}}{2 x - \frac{27}{5}}$$

Simplify

The second derivative [src]

         5                                     
-2100*log (-27/5 + 2*x)*(-6 + log(-27/5 + 2*x))
-----------------------------------------------
                             2                 
                 (-27 + 10*x)

$$- \frac{2100 \left(\log{\left(2 x - \frac{27}{5} \right)} - 6\right) \log{\left(2 x - \frac{27}{5} \right)}^{5}}{\left(10 x - 27\right)^{2}}$$

Simplify

The third derivative [src]

         4              /        2                                  \
42000*log (-27/5 + 2*x)*\15 + log (-27/5 + 2*x) - 9*log(-27/5 + 2*x)/
---------------------------------------------------------------------
                                        3                            
                            (-27 + 10*x)

$$\frac{42000 \left(\log{\left(2 x - \frac{27}{5} \right)}^{2} - 9 \log{\left(2 x - \frac{27}{5} \right)} + 15\right) \log{\left(2 x - \frac{27}{5} \right)}^{4}}{\left(10 x - 27\right)^{3}}$$

Simplify

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Derivative of 3*log(2x-5,4)^7

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